Question

Турист прошел часть пути и сделав привал увеличил скорость в 2 раза. найти отношение растояния до и после привала учитывая что на путь после привала он затратил в 1,5 раза меньше времени

Answer 1

Составь табличку:

до привала:
скорость V км/ч
время t ч
расстояние V*t км

после привала
скорость 2V км/ч
время 1,5t ч
расстояние 2V*1,5t=3Vt км

находим отношение
Vt/3Vt=1/3=1:3 (один к трем)

Answer 2

Problem Analysis

A tourist has traveled a certain distance and then took a break, during which they increased their speed by 2 times. The question is to find the ratio of the distance traveled before and after the break, considering that the time taken for the distance after the break is 1.5 times less than the time taken for the distance before the break.

Solution

Let's assume that the distance traveled before the break is D and the distance traveled after the break is d. The time taken for the distance before the break is T and the time taken for the distance after the break is t.

According to the given information, the tourist increased their speed by 2 times after the break. Therefore, the speed after the break is twice the speed before the break.

We can use the formula speed = distance / time to relate the distances and times before and after the break.

Before the break: - Speed before the break: s - Distance before the break: D - Time before the break: T

After the break: - Speed after the break: 2s (twice the speed before the break) - Distance after the break: d - Time after the break: t

Using the formula speed = distance / time, we can write the following equations:

Before the break: - s = D / T (equation 1)

After the break: - 2s = d / t (equation 2)

We are given that the time taken for the distance after the break is 1.5 times less than the time taken for the distance before the break. Mathematically, this can be expressed as:

- t = (2/3)T (equation 3)

To find the ratio of the distances before and after the break, we can divide equation 1 by equation 2:

- (D / T) / (d / t) = (D / T) / ((2s) / t)

Substituting equation 3 into the above equation:

- (D / T) / (d / t) = (D / T) / ((2s) / ((2/3)T))

Simplifying the equation:

- (D / T) / (d / t) = (D / T) / (2s / (2/3)T) - (D / T) / (d / t) = (D / T) / (2s * (3/2)T) - (D / T) / (d / t) = (D / T) / (3s) - (D / T) / (d / t) = D / (T * 3s)

Since we are looking for the ratio of the distances, we can simplify the equation further:

- (D / T) / (d / t) = D / (T * 3s) - (D / T) / (d / t) = D / (3sT) - (D / T) / (d / t) = D / (3D) - (D / T) / (d / t) = 1 / 3

Therefore, the ratio of the distance traveled before and after the break is 1:3.

Answer

The ratio of the distance traveled before and after the break is 1:3.